Question

A town in Wyoming wants to drill a geothermal well to provide district heating steam and hot water for its businesses and residences. After government subsides, the capital investment for the well is $1,500,000. Assuming end-of-year annual dollars savings in steam and hot water equal to 5 % of the investment cost of the well, and assuming the residual value of the well after 70 years is zero, determine the internal rate of return (as a percent) for this situation. The MARR of the town is 3% per year (Enter your answer as a number without the % sign.)

Answer 1

Answer::

here we determine internal rate of return by trial and error method. we find the rate where the npv become zero

initial investment = $1500000

annual saving = $1500000*5% = $75000

first we assume i = 4%

pv = -1500000 + $75000 ( P/A 4% 70 years)

​​​​​​= -1500000 + $75000 ( 23.3945)

= -1500000 + 1754588

= 254588

here npv positive so we try with higher rate rate i = 5%

npv = -1500000 + 75000 ( P/A 5% 70 years)

= -1500000 + 75000 ( 19.3427)

= -1500000 + 1450703

= -49298

so rate of return between 5% and 4%. but we get exactly by interpolation formula

4 + 254588 / 254588+49298 *1

4 + 254588 / 303886 *1

4 + 0.8377

4.83

so the internal rate of return is 4.81